The convergence of Algorithm REF  to the stationary point of the objective function in (17) can be established using the arguments considered by [1]} and Breheny and Huang [2]}. Both Wang [1]} and Breheny and Huang [2]} used the results of Lemma 3.1 and part (c) of Theorem 4.1 in [5]}. Although [5]} considered non-convex and non-differentiable objective function, the sufficient conditions for Lemma 3.1 and part (c) of Theorem 4.1 in [5]} can be extended to convex and continuously differentiable function.
